Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2010-11-11
Nonlinear Sciences
Exactly Solvable and Integrable Systems
31 Pages, 7 diagrams, submitted for consideration
Scientific paper
We propose a method to identify and classify evolution equations and systems that can be multipotentialised in given target equations or target systems. We refer to this as the {\it converse problem}. Although we mainly study a method for $(1+1)$-dimensional equations/system, we do also propose an extension of the methodology to higher-dimensional evolution equations. An important point is that the proposed converse method allows one to identify certain types of auto-B\"acklund transformations for the equations/systems. In this respect we define the {\it triangular-auto-B\"acklund transformation} and derive its connections to the converse problem. Several explicit examples are given. In particular we investigate a class of linearisable third-order evolution equations, a fifth-order symmetry-integrable evolution equation as well as linearisable systems.
Euler Marianna
Euler Norbert
No associations
LandOfFree
The converse problem for the multipotentialisation of evolution equations and systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The converse problem for the multipotentialisation of evolution equations and systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The converse problem for the multipotentialisation of evolution equations and systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-430839